the Alter Rebbe teaches in the Tanya that the true tzadik does not commit averot (sin) it is explained (in chapter 10 it seems to me) that the beinoni does not commit any avera then a fortiori the tsadik so how according on the fact that a tzadik does not make a mistake (as we can see in the tanya) we can explain that Adam Harishon (who is apparently a tzadik) committed an avera (moreover it is explained in the chassidus and kabala that the sin of Adam Harishon was to want to be at a level of creator like G.O.D who can create from nothing meayin leyesh I don't know if this precision is useful but that shows that the fault was quite serious)
I know that the question was also asked for moshe rabenou I saw a midrash that could give the answer of the midrash explaining that moshe rabenu was forced by Hashem for the sin of the rock. moreover the sin of the rock was not a "real sin", but only a sin at the level of moshe... perhaps it is the same thing for adam